The "repair disk Windows 7 64-bit" is not a disk to restore you to factory specifications unless you mislabeled it. It's to repair the Windows installation itself.
All the Acer's I have seen do have a recovery partition. You would access it through a menu in your list of programs or from an F key. I'm not sure exactly how on an Acer, but Google should tell you quickly. I'd look in my programs menu for Acer or Acer Recovery or similar terms. If you reboot, then F10 or alt-F10 may also lead to the recovery option.
Post a screen shot of Disk Management and we can probably identify the recovery partition on sight. It may be called "PQService".
If you restore from that partition, you shouldn't need that Product Key. If you do a clean install, you will need it.
Here's why I would not do the clean install without making recovery disks:
If you do a clean install, the recovery partition will likely be deleted. Even if not deleted, it may no longer work. The recovery disks are a substitute for the recovery partition and can be used even if the partition is gone. However, the disks are not as reliable as the partition---so you should always be prepared to do a clean install. If you ever have to deal with Acer support, they may want you to restore to factory specifications.